--- title: "Temporal variation in transmission during the COVID-19 outbreak" description: "To identify changes in the reproduction number, rate of spread, and doubling time during the course of the COVID-19 outbreak whilst accounting for potential biases due to delays in case reporting." status: in-progress rmarkdown_html_fragment: true redirect_from: - /topics/covid19/current-patterns-transmission/global-time-varying-transmission.html update: 2020-03-12 authors: - id: sam_abbott corresponding: true - id: joel_hellewell - id: james_munday - id: june_chun - id: robin_thompson - id: nikos_bosse - id: yung_wai - id: tim_russell - id: chris_jarvis - id: ncov-group - id: stefan_flasche - id: adam_kucharski - id: roz_eggo - id: seb_funk ---

Note: this is preliminary analysis, has not yet been peer-reviewed and is updated daily as new data becomes available. This work is licensed under a Creative Commons Attribution 4.0 International License. A summary of this report can be downloaded here

Summary

Aim: To identify changes in the reproduction number, rate of spread, and doubling time during the course of the COVID-19 outbreak whilst accounting for potential biases due to delays in case reporting.

Latest estimates as of the 2020-03-11

Global map


Figure 1: Global map of the expected change in daily cases based on data from the 2020-03-11. Note: only country level estimates are shown.

Summary of latest reproduction number and case count estimates


Figure 2: Cases with date of onset on the day of report generation and the time-varying estimate of the effective reproduction number (bar = 95% credible interval) based on data from the 2020-03-11. Countries/Regions are ordered by the number of expected daily cases and shaded based on the expected change in daily cases. The dotted line indicates the target value of 1 for the effective reproduction no. required for control and a single case required fror elimination.

Reproduction numbers over time in the six countries with the most cases currently


Figure 3: Time-varying estimate of the effective reproduction number (light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range) based on data from the 2020-03-11 in the countries/regions expected to have the highest number of incident cases. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence. The dotted line indicates the target value of 1 for the effective reproduction no. required for control.

Latest estimates summary table

Country/Region Cases with date of onset on the day of report generation Expected change in daily cases Effective reproduction no. Doubling time (days)
Italy 402 – 1968 Increasing 1.2 – 2.3 3.4 – Decreasing
Iran 364 – 1727 Increasing 1 – 1.7 6.6 – Decreasing
Spain 198 – 1434 Increasing 1.9 – 5.6 1.5 – 15
France 111 – 848 Increasing 1.5 – 3.7 2.3 – Decreasing
United States 72 – 507 Increasing 1.9 – 5.9 1.1 – Decreasing
South Korea 75 – 479 Unsure 0.6 – 1.2 Decreasing
Germany 50 – 373 Increasing 1.1 – 2.3 4.1 – Decreasing
Switzerland 45 – 352 Increasing 1.3 – 3.5 1.9 – Decreasing
Norway 24 – 189 Increasing 1.4 – 3.5 1.7 – Decreasing
Sweden 18 – 189 Increasing 1.3 – 3.5 1.7 – Decreasing
Netherlands 16 – 151 Increasing 1.2 – 3.2 2 – Decreasing
United Kingdom 14 – 124 Increasing 1.2 – 2.8 2.1 – 18
Austria 12 – 122 Increasing 1.3 – 3.5 2 – Decreasing
China 4 – 78 Decreasing 0.2 – 0.5 Decreasing
Belgium 7 – 77 Increasing 1 – 3 2.6 – Decreasing
Japan 26 – 74 Increasing 1.1 – 1.8 4.9 – Decreasing
China Excluding Hubei 2 – 55 Unsure 0.6 – 1.5 2.5 – Decreasing
Hubei 1 – 50 Decreasing 0.2 – 0.4 Decreasing
Hong Kong 1 – 34 Likely increasing 0.6 – 3.1 0.13 – Decreasing
Malaysia 2 – 34 Increasing 1 – 2.5 0.92 – Decreasing
Singapore 1 – 27 Increasing 0.9 – 2.2 1.8 – Decreasing


Table 1: Latest estimates of the number of cases by date of onset, the effective reproduction number, and the doubling time for the 2020-03-11 in each region included in the analysis. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate. China excludes Hubei.

Methods

Summary

Limitations

Detail

Data

We used partial line-lists from each region that contained the date of symptom onset, date of confirmation and import status (imported or local) for each case [3] where available. The region reports give details of the steps taken where this data were not available. Daily case counts by date of report were extracted from the World Health Organization (WHO) situation reports for every location considered [1,2]. The case counts (and partial line-lists where available) were used to assemble the daily number of local and imported cases. Where the partial line-lists and case counts disagreed, it was assumed that the partial line-lists were correct and the WHO case counts were adjusted so that the overall number of cases occurring remained the same but the number of local cases being adjusted as needed.

Adjusting for reporting delays

Reporting delays for each country were estimated using the corresponding partial line-list of cases. The reporting delay could not be estimated from line-list data for all regions. Region specific details are given in the individual regional reports. The estimated reporting delay was assumed to remain constant over time in each location. We fitted an exponential distribution adjusted for censoring [7] to the observed delays using stan [8]. We then took 1000 samples from the posterior distribution of the rate parameter for the exponential delay distribution and constructed a distribution of possible onset dates for each case based on their reporting date. To prevent spuriously long reporting delays, we re-sampled delays that were greater than the maximum observed delay in the observed data.

To account for censoring, i.e. cases that have not yet been confirmed but will show up in the data at a later time, we randomly sampled the true number of cases (including those not yet confirmed) assuming that the reported number of cases is drawn from a binomial distribution, where each case has independent probability \(p_i\) of having been confirmed, \(i\) is the number of days of the symptom onset before the report maximum observed report delay, and \(p_i\) is the cumulative distribution of cases that are confirmed by day \(i\) after they develop symptoms. We did not account for potential reporting biases that might occur due to changes in the growth rate of the outbreak over time.

Statistical analysis

We used the inferred number of cases to estimate the reproduction number on each day using the EpiEstim R package [4]. This uses a combination of the serial interval distribution and the number of observed cases to estimate the reproduction number at each time point [10,11], which were then smoothed using a 7-day time window. We assumed that the serial interval was uncertain with a mean of 4.7 days (95% CrI: 3.7, 6.0) and a standard deviation of 2.9 days (95% CrI: 1.9, 4.9) [6]. We used a common prior for the reproduction number with mean 2.6 and a standard deviation of 2 (inflated from 0.5 found in the reference) [12]. Where data was available, we used EpiEstim to adjust for imported cases [5]. The expected change in daily cases was defined using the proportion of samples with a reproduction number less than 1 (subcritical). It was assumed that if less than 5% of samples were subcritical then an increase in cases was definite, if less than 20% of samples were subcritical then an increase in cases was likely, if more than 80% of samples were subcritical then a decrease in cases was likely and if more than 95% of samples were subcritical then a decrease in cases was definite. For countries/regions with between 20% and 80% of samples being subcritical we could not make a statement about the likely change in cases (defined as unsure).

We estimated the rate of spread (\(r\)) using linear regression with time as the only exposure and logged cases as the outcome for the overall course of the outbreak [13]. The adjusted R^2 value was then used to assess the goodness of fit. In order to account for potential changes in the rate of spread over the course of the outbreak we used a 7-day sliding window to produce time-varying estimates of the rate of spread and the adjusted R^2. The doubling time was then estimated using \(\text{ln}(2) \frac{1}{r}\) for each estimate of the rate of spread.

We report the 95% confidence intervals for all measures using the 2.5% and 97.5% quantiles. The analysis was conducted independently for all regions and is updated daily as new data becomes available. Confidence in our estimates is shown using the proportion of data that were derived using binomial upscaling.

Regional reports

Italy

Summary


Figure 4: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 402 – 1968
Expected change in daily cases Increasing
Effective reproduction no. 1.2 – 2.3
Rate of spread -0.082 – 0.2
Doubling time (days) 3.4 – Decreasing
Adjusted R-squared -0.18 – 0.99


Table 4: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 5: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • The reporting delay was estimated using a combined European linelist (including cases from Germany, France, Italy, Austria, the Netherlands, Belgium, and Spain).

Iran

Summary


Figure 7: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 364 – 1727
Expected change in daily cases Increasing
Effective reproduction no. 1 – 1.7
Rate of spread -0.18 – 0.11
Doubling time (days) 6.6 – Decreasing
Adjusted R-squared -0.32 – 0.86


Table 5: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 8: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • The reporting delay was estimated using a combined European linelist (including cases from Germany, France, Italy, Austria, the Netherlands, Belgium, and Spain).

Spain

Summary


Figure 10: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 198 – 1434
Expected change in daily cases Increasing
Effective reproduction no. 1.9 – 5.6
Rate of spread 0.045 – 0.46
Doubling time (days) 1.5 – 15
Adjusted R-squared 0.043 – 0.98


Table 6: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 11: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • The reporting delay was estimated using a combined European linelist (including cases from Germany, France, Italy, Austria, the Netherlands, Belgium, and Spain).

France

Summary


Figure 13: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 111 – 848
Expected change in daily cases Increasing
Effective reproduction no. 1.5 – 3.7
Rate of spread -0.11 – 0.3
Doubling time (days) 2.3 – Decreasing
Adjusted R-squared -0.2 – 0.95


Table 7: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 14: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • The reporting delay was estimated using a combined European linelist (including cases from Germany, France, Italy, Austria, the Netherlands, Belgium, and Spain).

United States

Summary


Figure 16: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 72 – 507
Expected change in daily cases Increasing
Effective reproduction no. 1.9 – 5.9
Rate of spread -0.37 – 0.63
Doubling time (days) 1.1 – Decreasing
Adjusted R-squared -0.11 – 0.94


Table 8: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 17: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • The reporting delay was estimated using a combined European linelist (including cases from Germany, France, Italy, Austria, the Netherlands, Belgium, and Spain).

South Korea

Summary


Figure 19: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 75 – 479
Expected change in daily cases Unsure
Effective reproduction no. 0.6 – 1.2
Rate of spread -0.24 – -0.015
Doubling time (days) Decreasing
Adjusted R-squared 0.031 – 0.95


Table 9: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 20: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

Germany

Summary


Figure 22: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 50 – 373
Expected change in daily cases Increasing
Effective reproduction no. 1.1 – 2.3
Rate of spread -0.35 – 0.17
Doubling time (days) 4.1 – Decreasing
Adjusted R-squared -0.25 – 0.76


Table 10: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 23: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

Switzerland

Summary


Figure 25: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 45 – 352
Expected change in daily cases Increasing
Effective reproduction no. 1.3 – 3.5
Rate of spread -1.8 – 0.37
Doubling time (days) 1.9 – Decreasing
Adjusted R-squared -0.22 – 0.75


Table 11: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 26: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • The reporting delay was estimated using a combined European linelist (including cases from Germany, France, Italy, Austria, the Netherlands, Belgium, and Spain).

Norway

Summary


Figure 28: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 24 – 189
Expected change in daily cases Increasing
Effective reproduction no. 1.4 – 3.5
Rate of spread -0.084 – 0.41
Doubling time (days) 1.7 – Decreasing
Adjusted R-squared -0.19 – 0.85


Table 12: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 29: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • The reporting delay was estimated using a combined European linelist (including cases from Germany, France, Italy, Austria, the Netherlands, Belgium, and Spain).

Sweden

Summary


Figure 31: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 18 – 189
Expected change in daily cases Increasing
Effective reproduction no. 1.3 – 3.5
Rate of spread -0.21 – 0.42
Doubling time (days) 1.7 – Decreasing
Adjusted R-squared -0.33 – 0.91


Table 13: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 32: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • The reporting delay was estimated using a combined European linelist (including cases from Germany, France, Italy, Austria, the Netherlands, Belgium, and Spain).

Netherlands

Summary


Figure 34: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 16 – 151
Expected change in daily cases Increasing
Effective reproduction no. 1.2 – 3.2
Rate of spread -0.24 – 0.35
Doubling time (days) 2 – Decreasing
Adjusted R-squared -0.25 – 0.94


Table 14: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 35: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • The reporting delay was estimated using a combined European linelist (including cases from Germany, France, Italy, Austria, the Netherlands, Belgium, and Spain).

United Kingdom

Summary


Figure 37: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 14 – 124
Expected change in daily cases Increasing
Effective reproduction no. 1.2 – 2.8
Rate of spread 0.039 – 0.34
Doubling time (days) 2.1 – 18
Adjusted R-squared 0.087 – 0.96


Table 15: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 38: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • The reporting delay was estimated using a combined European linelist (including cases from Germany, France, Italy, Austria, the Netherlands, Belgium, and Spain).

Austria

Summary


Figure 40: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 12 – 122
Expected change in daily cases Increasing
Effective reproduction no. 1.3 – 3.5
Rate of spread -0.082 – 0.34
Doubling time (days) 2 – Decreasing
Adjusted R-squared -0.17 – 0.88


Table 16: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 41: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • The reporting delay was estimated using a combined European linelist (including cases from Germany, France, Italy, Austria, the Netherlands, Belgium, and Spain).

China

Summary


Figure 43: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 4 – 78
Expected change in daily cases Decreasing
Effective reproduction no. 0.2 – 0.5
Rate of spread -0.47 – -0.049
Doubling time (days) Decreasing
Adjusted R-squared 0.13 – 0.96


Table 17: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 44: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • Cases in Hubei were excluded from the china case counts.
  • Data is only used from the 2nd of February onwards.

Belgium

Summary


Figure 46: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 7 – 77
Expected change in daily cases Increasing
Effective reproduction no. 1 – 3
Rate of spread -0.39 – 0.27
Doubling time (days) 2.6 – Decreasing
Adjusted R-squared -0.3 – 0.92


Table 18: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 47: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • The reporting delay was estimated using a combined European linelist (including cases from Germany, France, Italy, Austria, the Netherlands, Belgium, and Spain).

Japan

Summary


Figure 49: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 26 – 74
Expected change in daily cases Increasing
Effective reproduction no. 1.1 – 1.8
Rate of spread -0.078 – 0.14
Doubling time (days) 4.9 – Decreasing
Adjusted R-squared -0.16 – 0.66


Table 19: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 50: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • Cases linked to the Diamond Princess were removed manually from the case counts on the 5th of February.

China Excluding Hubei

Summary


Figure 52: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 2 – 55
Expected change in daily cases Unsure
Effective reproduction no. 0.6 – 1.5
Rate of spread -2 – 0.28
Doubling time (days) 2.5 – Decreasing
Adjusted R-squared -0.17 – 0.49


Table 20: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 53: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

Hubei

Summary


Figure 55: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 1 – 50
Expected change in daily cases Decreasing
Effective reproduction no. 0.2 – 0.4
Rate of spread -0.63 – -0.11
Doubling time (days) Decreasing
Adjusted R-squared 0.23 – 0.96


Table 21: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 56: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • Data is only used from the 2nd of February onwards.

Hong Kong

Summary


Figure 58: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 1 – 34
Expected change in daily cases Likely increasing
Effective reproduction no. 0.6 – 3.1
Rate of spread -4.6 – 5.5
Doubling time (days) 0.13 – Decreasing
Adjusted R-squared -0.25 – 0.58


Table 22: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 59: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

Malaysia

Summary


Figure 61: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 2 – 34
Expected change in daily cases Increasing
Effective reproduction no. 1 – 2.5
Rate of spread -0.46 – 0.75
Doubling time (days) 0.92 – Decreasing
Adjusted R-squared -0.36 – 0.59


Table 23: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 62: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

Singapore

Summary


Figure 64: A.) Cases by date of report (bars) and estimated cases by date of onset. B.) Time-varying estimate of the effective reproduction number. Light grey ribbon = 95% credible interval. Dark grey ribbon = the interquartile range. Based on data from the 2020-03-11. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Estimate
Cases with date of onset on the day of report generation 1 – 27
Expected change in daily cases Increasing
Effective reproduction no. 0.9 – 2.2
Rate of spread -0.46 – 0.37
Doubling time (days) 1.8 – Decreasing
Adjusted R-squared -0.18 – 0.62


Table 24: Latest estimates of the number of cases by date of onset, the expected change in daily cases, the effective reproduction number, the rate of spread, the doubling time, and the adjusted R-squared of the exponential fit for the 2020-03-11. Based on the last 7 days of data. The 95% credible interval is shown for each numeric estimate.

Time-varying rate of spread and doubling time


Figure 65: A.) Time-varying estimate of the rate of spread, B.) Time-varying estimate of the doubling time in days (note that when the rate of spread is negative the doubling time is assumed to be infinite), C.) The adjusted R-squared estimates indicating the goodness of fit of the exponential regression model (with values closer to 1 indicating a better fit). Based on data from the 2020-03-11. Light grey ribbon = 95% credible interval; dark grey ribbon = the interquartile range. Confidence in the estimated values is indicated by shading with reduced shading corresponding to reduced confidence.

Implementation details

  • Line-list data was only available until the 18th of February for Singapore.

Updates

2020-03-11

2020-03-07

References

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4 Cori A. EpiEstim: Estimate time varying reproduction numbers from epidemic curves. 2019. https://CRAN.R-project.org/package=EpiEstim

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